Code

This example help us to understand the principle of the PAC concept, that as we can see tries to reduce the data, so this could helps us to improve on our performance.

load magic2.txt; %We read the database form a TXT
figure('Name','DataSet', 'NumberTitle','off');
plot(magic2(1,:),'o:r', 'LineWidth',2); %We plot the original data 
hold; 
plot(magic2(19020,:),'o:b', 'LineWidth',2);
title('Dos clases Magic DataSet ')
xlabel('Muestra');
ylabel('Amplitud (mV)');
nobservations=size(magic2,1) %We set the number of observations and the number of features. 
nfeatures=size(magic2,2)

c = linspace(1,10,length(magic2(:,1)));
figure('Name','Magic DataSet', 'NumberTitle','off');
scatter3(magic2(:,1),magic2(:,2),magic2(:,3),[],c);
title('Magic DataSet entero')
xlabel('1^{st} feature (mV)');
ylabel('2^{nd} feature (mV)');
zlabel('3^{rd} feature (mV)');

[coeff,score,latent,tsquare] = princomp(zscore(magic2)); %We run the principle components function

percent=latent./sum(latent)*100;
figure('Name','PCA Valores Propios', 'NumberTitle','off');
plot(1:length(latent),percent,'o:b', 'LineWidth',2);
grid;
xlabel('Valores Propios');
ylabel('Peso (%)');

figure('Name','3D Reducci?n PC', 'NumberTitle','off'); %Print the new data on a 3d graph dimension 
scatter3(score(:,1),score(:,2),score(:,3),[]);
title('Reducci?n por PCA');
xlabel('1^{st} feature (mV)');
ylabel('2^{nd} feature (mV)');
zlabel('3^{rd} feature (mV)');

figure('Name','Reducido vs NO reducido', 'NumberTitle','off'); %Print both data so we can compare. 
subplot(1,2,1); 
scatter(score(:,1),score(:,2),[]);
title('Reduced set');
xlabel('1^{st} feature (mV)');
ylabel('2^{nd} feature (mV)');
subplot(1,2,2); 
scatter(magic2(:,1),magic2(:,2),[]);
title('NOT reduced set');
xlabel('1^{st} feature (mV)');
ylabel('2^{nd} feature (mV)');

fid=fopen('MyFile2.txt','w');
fprintf(fid, '%f %f %f \n', score(:,1),score(:,2),score(:,3));
fclose(fid);